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Simplifying 9x2 + 11x + -124 = 0 Reorder the terms: -124 + 11x + 9x2 = 0 Solving -124 + 11x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -13.77777778 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '13.77777778' to each side of the equation. -13.77777778 + 1.222222222x + 13.77777778 + x2 = 0 + 13.77777778 Reorder the terms: -13.77777778 + 13.77777778 + 1.222222222x + x2 = 0 + 13.77777778 Combine like terms: -13.77777778 + 13.77777778 = 0.00000000 0.00000000 + 1.222222222x + x2 = 0 + 13.77777778 1.222222222x + x2 = 0 + 13.77777778 Combine like terms: 0 + 13.77777778 = 13.77777778 1.222222222x + x2 = 13.77777778 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = 13.77777778 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 13.77777778 + 0.3734567900 Combine like terms: 13.77777778 + 0.3734567900 = 14.15123457 0.3734567900 + 1.222222222x + x2 = 14.15123457 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 14.15123457 Calculate the square root of the right side: 3.761812671 Break this problem into two subproblems by setting (x + 0.611111111) equal to 3.761812671 and -3.761812671.Subproblem 1
x + 0.611111111 = 3.761812671 Simplifying x + 0.611111111 = 3.761812671 Reorder the terms: 0.611111111 + x = 3.761812671 Solving 0.611111111 + x = 3.761812671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 3.761812671 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 3.761812671 + -0.611111111 x = 3.761812671 + -0.611111111 Combine like terms: 3.761812671 + -0.611111111 = 3.15070156 x = 3.15070156 Simplifying x = 3.15070156Subproblem 2
x + 0.611111111 = -3.761812671 Simplifying x + 0.611111111 = -3.761812671 Reorder the terms: 0.611111111 + x = -3.761812671 Solving 0.611111111 + x = -3.761812671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -3.761812671 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -3.761812671 + -0.611111111 x = -3.761812671 + -0.611111111 Combine like terms: -3.761812671 + -0.611111111 = -4.372923782 x = -4.372923782 Simplifying x = -4.372923782Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.15070156, -4.372923782}
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